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| Mirrors > Home > MPE Home > Th. List > jcad | Structured version Visualization version GIF version | ||
| Description: Deduction conjoining the consequents of two implications. Deduction form of jca 511 and double deduction form of pm3.2 469 and pm3.2i 470. (Contributed by NM, 15-Jul-1993.) (Proof shortened by Wolf Lammen, 23-Jul-2013.) |
| Ref | Expression |
|---|---|
| jcad.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
| jcad.2 | ⊢ (𝜑 → (𝜓 → 𝜃)) |
| Ref | Expression |
|---|---|
| jcad | ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜃))) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | jcad.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
| 2 | jcad.2 | . 2 ⊢ (𝜑 → (𝜓 → 𝜃)) | |
| 3 | pm3.2 469 | . 2 ⊢ (𝜒 → (𝜃 → (𝜒 ∧ 𝜃))) | |
| 4 | 1, 2, 3 | syl6c 70 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜃))) |
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